Global synchronization criteria for a class of third-order non-autonomous chaotic systems via linear state error feedback control

Applied Mathematical Modelling

Volumn 34, Issue 12, 2010, Pages 4161-4170

  Chen, Yun ^a   Wu, Xiaofeng ^a,b   Gui, Zhifang ^a  

^a NAVAL UNIVERSITY OF ENGINEERING   (China)

^b Guangzhou Naval Academy   (China)

Author keywords

Chaos; Generalized Lorenz system; Global synchronization; Gyrostat system; Non autonomous chaotic system

Indexed keywords

GENERALIZED LORENZ SYSTEM; GLOBAL SYNCHRONIZATION; GYROSTAT SYSTEM; GYROSTATS; NONAUTONOMOUS;

ALGEBRA; DELAY CONTROL SYSTEMS; FEEDBACK; FEEDBACK CONTROL; FREQUENCY SELECTIVE FADING; FUZZY CONTROL; LINEAR MATRIX INEQUALITIES; STATE FEEDBACK; SYNCHRONIZATION;

CHAOTIC SYSTEMS;

EID: 77954031400     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2010.04.013     Document Type: Article

References (39)

1. Lakshmanman M., Murali K. Chaos in Nonlinear Oscillators: Controlling and Synchronization 1996, World Scientific Press, Singapore.
2. Blasius B., Huppert A., Stone L. Complex dynamics and phase synchronization in spatially extended ecological system. Nature 1999, 399:354-359.
3. Mu X., Pei L. Synchronization of the near-identical chaotic systems with the unknown parameters. Appl. Math. Model. 2010, 34:1788-1797.
4. Ge Z.M., Lin T.N. Chaos, chaos control and synchronization of a gyrostat system. J. Sound Vib. 2002, 251:519-542.
5. Jiang G.P., Tang W.K.S. A global synchronization criterion for coupled chaotic systems via unidirectional linear error feedback approach. Int. J. Bifurcat. Chaos 2002, 12:2239-2253.
6. Jiang G.P., Chen G., Tang W.K.S. A new criterion for chaos synchronization using linear state feedback control. Int. J. Bifurcat. Chaos 2003, 13(8):2343-2351.
7. Jiang G.P., Tang W.K.S., Chen G. A simple global synchronization criterion for coupled chaotic systems. Chaos Soliton Fract. 2003, 15:925-935.
8. Sun J., Zhang Y. Some simple global synchronization criterions for coupled time-varied chaotic systems. Chaos Soliton Fract. 2004, 19:93-98.
9. Ge Z.M., Chang C.M. Chaos synchronization and parameters identification of single time scale brushless DC motors. Chaos Soliton Fract. 2004, 20:883-903.
10. Ge Z.M., Leu W.Y. Chaos synchronization and parameter identification for loudspeaker systems. Chaos Soliton Fract. 2004, 21:1231-1247.
11. Ge Z.M., Cheng J.W. Chaos synchronization and parameter identification of three time scales brushless DC motor system. Chaos Soliton Fract. 2005, 24:597-616.
12. Haeri M., Khademian B. Comparison between different synchronization methods of identical chaotic systems. Chaos Soliton Fract. 2006, 29:1002-1022.
13. Chen H.H. Global synchronization of chaotic systems via linear balanced feedback control. Appl. Math. Comput. 2007, 186:923-931.
14. Mahmoud G.M., Aly S.A., Farghaly A.A. On chaos synchronization of a complex two coupled dynamos system. Chaos Soliton Fract. 2007, 33:178-187.
15. Wu X., Chen G., Cai J. Chaos synchronization of the master-slave generalized Lorenz systems via linear state error feedback control. Physica D 2007, 229:52-80.
16. Sarasola C., Torrealdea F.J., Anjou A.D., Moujahid A., Grana M. Feedback synchronization of chaotic systems. Int. J. Bifurcat. Chaos 2008, 13(1):177-191.
17. Wang F., Liu C. A new criterion for chaos and hyperchaos synchronization using linear feedback control. Phys. Lett. A 2006, 360:274-278.
18. Han X., Lu J.A., Wu X. Adaptive feedback synchronization of Lü system. Chaos Soliton Fract. 2004, 22:221-227.
19. Yassen M.T. Controlling chaos and synchronization for new chaotic system using linear feedback control. Chaos Soliton Fract. 2005, 26:913-920.
20. Wu X.F., Zhao Y. Frequency domain criterion for chaos synchronization of Lur'e systems via linear state error feedback control. Int. J. Bifurcat. Chaos 2005, 15(4):1445-1454.
21. Liao X., Chen G., Xu B., Shen Y. On global exponential synchronization of Chua circuits. Int. J. Bifurcat. Chaos 2005, 15(7):2227-2234.
22. Wu X., Cai J., Zhao Y. Some new algebraic criteria for chaos synchronization of chua's circuits by linear state error feedback control. Int. J. Circ. Theor. Appl. 2006, 34.
23. Wu X., Cai J., Wang M. Master-slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control. J. Sound Vib. 2006, 295:378-387.
24. Čelikovský S., Chen G. On a generalized Lorenz canonical form of chaotic systems. Int. J. Bifurcat. Chaos 2002, 12:1789-1812.
25. Lü J., Chen G., Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int. J. Bifurcat. Chaos 2004, 14:1507-1537.
26. Huang D., Zhang L. Dynamics of the Lorenz-Robbins system with control. Physica D 2006, 218:131-138.
27. Agiza H.N. Chaos synchronization of two coupled dynamos systems with unknown system parameters. Int. J. Mod. Phys. C 2004, 15(6):873-883.
28. Liu W.B., Chen G. A new chaotic system and its generation. Int. J. Bifurcat. Chaos 2003, 12:261-267.
29. Ge Z.M., Chang C.M., Chen Y.S. Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems. Chaos Soliton Fract. 2006, 27:1298-1315.
30. Jia Q. Chaos control and synchronization of the Newton-Leipnik chaotic system. Chaos Soliton Fract. 2008, 35:814-824.
31. Ge Z.M., Lee C.I., Chen H.H., Lee S.C. Non-linear dynamics and chaos control of a damped satellite with partially-filled liquid. J. Sound Vib. 1998, 217:807-825.
32. Yassen M.T. Adaptive control and synchronization of a modified Chua's circuit system. Appl. Math. Comput. 2003, 135:113-128.
33. Fostin H., Bowong S., Daafouz J. Adaptive synchronization of two chaotic systems consisting of modified Van der Pol-Duffing and Chua oscillators. Chaos Soliton Fract. 2005, 26:215-229.
34. Li Z., Xu D. Stability criterion for projective synchronization in three-dimensional chaotic systems. Phys. Lett. A 2001, 282:175-179.
35. Li Y., Liu X., Zhang H. Dynamical analysis and impulsive control of a new hyperchaotic system. Math. Comput. Model. 2005, 42:1359-1374.
36. Chen Y., Wu X. Global chaos synchronization of nonautonomous gyrostat systems via variable substitution control. Int. J. Bifurcat. Chaos 2008, 18(12):3719-3730.
37. Curran P.F., Chua L.O. Absolute stability theory and the synchronization problem. Int. J. Bifurcat. Chaos 1997, 7:1357-1382.
38. Slotine J.E., Li W.P. Applied Nonlinear Control 2004, China Machine Press, Beijing.
39. Horn R.A., Johnson C.R. Matrix Analysis 1985, Cambridge University Press, Cambridge.